Temperature Tunability of Dielectric/ Liquid Crystal / Dielectric Photonic Crystal...

Islamic Azad University

Journal of

Optoelectronical Nanostructures

Autumn 2017 / Vol. 2, No. 4

Temperature Tunability of Dielectric/ Liquid Crystal /

Dielectric Photonic Crystal Structures

Tahere Froutan fard kobar olia1, Ali Vahedi

*, 1

1 Department of Physics, Tabriz Branch, Islamic Azad University, Tabriz, Iran.

(Received 17 Sep. 2017; Revised 11 Oct. 2017; Accepted 25 Nov. 2017; Published 15 Dec. 2017) Abstract: Recently, photonic crystals doped with liquid crystal (LC) material have gained much research interest. In this article new ternary one-dimensional photonic

crystal introduced and studied. The liquid crystal layer of 5CB and 5PCH is sandwiched

by two dielectric layers. For the first time, we use four structures SiO2/UCF35/CaF2,

SiO2/5CB/CaF2, NFK51/UCF35/NPSK53 and NFK51/5CB/NPSK53. The effect of temperature on transfer band gap of these photonic crystals is investigated with

transferred matrix method. The results show that in all four structures PBG for

extraordinary ray (ne) is very large than ordinary ray (no) and with increasing of

temperature, PBG shifts to red wavelength. PBG width is very vast and variation of the

figure with respect temperature is very sharp for SiO2/UCF35/CaF2 structure. Also, the

suggested design takes high tunability due to the infiltration of the LC material. One can

use the proposed structure as temperature sensing device, narrow band optical filter and

in many optical systems.

Keywords: photonic crystal, liquid crystal, temperature sensing device, ternary

one-dimensional.

1. INTRODUCTION

Photonic crystals (PhCs) are micro and nano-size structures, where the

refractive index or permittivity of different material is periodic. Photonic crystal

has photonic band gap (PBG). Therefore, the electromagnetic wave with the

frequency in the band gap cannot be transmitted [1- 4]. This is one of the most

basic characteristics of the photonic crystal. Photonic nanostructure devices,

photonic chips, novel lasers, etc., will presently become available. The worlds of

photonic crystals are now expanding to various science and technology areas

such as quantum computing, bio-photonics and communications [5-9]. A

photonic crystal is described by Bragg reflection and play an important role in

* Corresponding author. Email: [email protected]

58 * Journal of Optoelectronical Nanostructures Autumn 2017 / Vol. 2, No. 4

studies of laser, optical filters [2-3], optical sensors [10] and temperature sensors

[5-7]. PhC devices are routinely fabricated and their optical properties may be

adjusted by modifying the size or structure design. But, PhC-based structures are

often lacking in flexibility and tunability, there are still a few factors that limit

the use of PhCs in real devices. Therefore, the research has focused on

possibility of increasing the device fine-tune either by correcting or by

controlling the optical properties of the PhC to compensate either the

temperature sensitivity or the imperfections of the PhC itself. The optical

properties of PhCs can be modified by changing the optical length and refractive

index of the PhC Structure. The common tuning methods used in optoelectronic

devices can be applied to adjust its refractive index by temperature, optical

pumping or applying an external magnetic or electric field [7-12].

Among the several techniques that have been proposed, infiltrating some layer

of a PhC with an organic material that has a tunable refractive index (e.g. liquid

crystals, polymers, liquids, and colloidal quantum dots) has proved to be one of

the most hopeful approaches for both trimming and tuning [13-15]. The

injection of liquid crystals (LC) in PhCs structure naturally from the following

properties of LC:

- They offer a large variety of interesting optical properties both in the visible

and in the near-infrared spectral regions that often depend on the molecular

organization;

- There exist a wide palette of different molecular organizations depending on

the molecule interactions. The complex thermodynamic properties of such

molecular mixtures enable one to easily change the molecular order by changing

the temperature, applying an electric field and thus, the optical properties of the

material itself. In particular, the potential of PhC infiltration with nematic liquid

crystals (LCs) has been largely demonstrated for one, two and three-dimensional

(1D, 2D and 3D) PhCs. Therefore, besides their classical fields of application,

LCs are also having a strong impact in the PhC field [15-18]. In nematic LC, if

the electric field of light is perpendicularly or parallel polarized to the axis of the

LC molecules, light experiences the ordinary refractive index (no) or the

extraordinary refractive index (ne), respectively. The optical response of a PhC

infiltrated with nematic LCs can be either trimmed or tuned by applying an

external electric field which modifies the orientation of molecules with respect

to the polarization direction of a light beam propagating through it. Moreover,

when the temperature is increased above the nematic-isotropic (clearing point)

phase transition temperature, the molecular order is destroyed and the LC is in

its isotropic phase, its optical properties are thus characterized by an isotropic

refractive index (ni) that is independent of the molecule orientation [18-19].

Recently, PhCs doped with liquid crystal (LC) material have gained much

Temperature Tunability of Dielectric/ Liquid Crystal / Dielectric Photonic Crystal … * 59

research interest [20-21]. Additional, 1D PhCs with central LC defects have

been roughly reported. Ozaki et al. have studied the tunability of the defect

modes of 1D PhCs with central nematic LC (NLC) [22] and dye-doped NLC

[23] defects. In these investigations, the studied 1D PhC has a bandgap range

from the wavelength of 590 nm to 710 nm. Furthermore, the spectral properties

of an electrically tuneable 1D PhC infiltrated with twisted-NLC have been

reported by Lin et al [24]. Moreover, the electrical and thermal tuning of 1D

NLC PhC has been studied experimentally with bandgap range from 11 -18 μm

[25].

In the present article, we consider a liquid crystal material as one of the layers

of a ternary one-dimensional photonic crystal. The dielectric property of liquid

crystals depends not only on temperature but also on wavelength. The suggested

design has also high tunability due to infiltration of the LC material. Further, the

effects of the polarization angle of light incident and temperature on the

transmission characteristics of the suggested design are investigated.

2. BASIC EQUATION

One-dimensional ternary dielectric/ liquid crystal / dielectric Photonic crystal

(LDPCs) structure is shown in Fig. (1). In this structure liquid crystal layer

sandwich with two dielectric layers.

Fig 1. Structure of the one-dimensional photonic crystal with LC (blue) layers. Here,

φ denotes the angle between the optical axis of the anisotropic LC layer and the x-axis

[33].

We assume that the dielectric layers are in the x–y plane and the z-direction is

normal to the interface of each layer. where φ is the angle between the optical

axis of the liquid crystal layer and the x-axis. We know thickness and refractive

index of the medium are changed with temperatures variation. Modification of

----------------------


thickness and refractive index for dielectrics layers are [26]:

Tdd (1) Tnn (2)

where , and T represent thermal expansion, thermo-optic coefficient for

dielectrics and temperature variation of LC respectively. From the Vuks semi-

empirical equation relating the refractive indices with the molecular

polarizabilities for anisotropic materials [27]:

2

2

1 432

eoeo

nN

n

(3)

In Eq. (3), no and ne are refractive indices for the ordinary and extraordinary

ray, respectively, N is the number of molecules per unit volume, eo is the

molecular polarizability, and 2n is defined as:

2 2

2 2

3e on nn

(4)

In Eq. (4), ne and no are coupled together. To disclose this relating, we should

decouple ne from no by solving Eq. (3). Replacing Eq. (4) to Eq. (3) and

separating ne and no, we derive: 2 2

23 2 3( )4 44

1 13 3

e o

e

NSNn T

N N

(5)

223 2 3( )4 44

1 13 3

e o

o

NSNn T

N N

(6)

Where N is small, Birefringence of an LC material is defined as n .

Subtracting Eq. (6) from Eq. (5), we find:

2

( )4

13

e oNSn T

N

(7)

The refractive indices equation has the following simple terms:

23e

n n n (8)


13o

n n n (9)

In theory, both ne and no are functions of wavelength and temperature. The

wavelength effect has been talked widely [19,28]. Here, we focused on the

temperature effects. According to our treatments and fitting results, the average

refractive index decreases linearly as the temperature increases:

( )n T A BT (10)

Equation (10) has a negative gradient. The value of B is around 10-4 K-1. In

contrast, birefringence is dependent on the order parameter S. Based on Haller’s

approximation, the order parameter can be approximated as CT

TS 1 thus, the

temperature-dependent birefringence has the following form:

cT

Tnn 10

(11)

In Eq. (11), 0)( n is the LC birefringence in the crystalline phase (or KT

O0 ),

the exponent is a material constant, and Tc is the clearing temperature of the

LC materials under investigation. Substituting Eqs. (10) and (11) back to Eqs.

(8) and (9), one can derive the four-parameter model for describing the

temperature effect on the LC refractive indices [19,27]:

0

2( ) 1

3e c

n Tn T A BT

T

(12)

0( ) 1

3o c

n Tn T A BT

T

(13)

By taking temperature derivatives of Eqs. (12) and (13), the temperature

gradient for ne and no can be derived:

10

21

3e

c c

ndn TB

dt T T

(14)

10 1

3o

c c

ndn TB

dt T T

(15)


In this work, we use two different liquid crystals: 5CB and UCF35. At room

temperature, the Physical properties, clearing temperatures and birefringence, of

the compounds are shown in the table (1).

Table 1. Physical properties of 5CB and UCF35 compounds at 589 nm [29].

TC(0k) 0)( n )(1KB A LC

6.306 1889.0 3505.0 41079.5 7674.1 CB5

3.368 2719.0 5727.0 41032.5 8187.1 35UCF

The Physical properties of dielectrics (optical glass), are shown in table (2).

Table 2. Physical properties of dielectrics [26].

)( 01c )( 01k

n Dielectric

6109.11 61055.0 444.1 2SiO

6107.11 61019 4226.1 2CaF

61013 6107.5 486.1 51NFK

6104.9 6103.2 620.1 53NPSK

The transmission properties of one-dimensional PC consisting of LC are

distributed in a transparent matrix. Let us consider a one-dimensional ternary

PC, with N elementary cells with lattice constant 2SiO . Each cell consists of one

dielectric layer of width 1d with refractive index 1n and one layer of LC of

width 2d with refractive index equal to en or on (uniaxial crystals) and one

dielectric n3 with width 3d and refractive index 3n . The lattice constant

is 321 ddda . To compute the PBG in the transmission spectra due to the

temperature and light incident angle dependence with respect to wavelength, we

use the transfer matrix method (TMM) [30-31]. The relative permittivity of the

layers A and B are denoted by A and B respectively. The dielectric tensor of the

anisotropic liquid crystal layer in the coordinate system shown in Figure (1) is

[32]:


𝜀𝐷 =

𝑛𝑜2𝑆𝑖𝑛2𝜑 + 𝑛𝑒

2𝐶𝑜𝑠2𝜑1

2(𝑛𝑒

2 − 𝑛𝑜2)𝑆𝑖𝑛2𝜑 0

1

2(𝑛𝑒

2 − 𝑛𝑜2)𝑆𝑖𝑛2𝜑 𝑛𝑜

2𝐶𝑜𝑠2𝜑 + 𝑛𝑒2𝑆𝑖𝑛2𝜑 0

0 0 𝑛𝑜2

The transmission properties of the structure are studied using the well-known 4

× 4 transfer matrix formulation [32-33] which is a very useful method in the

presence anisotropic materials. In such cases, it is assumed that the

electromagnetic wave consists of four partial waves and mode coupling

(between TE and TM modes) takes place at the interfaces of the anisotropic

material. however, for the cases of φ = 0 and φ = 90◦, the dielectric tensor of the

LC defect layer will be diagonal and a simpler 2×2 transfer matrix method can

be used to investigate the optical properties of the structure [33]. Each layer of

PC has its own transfer matrix, and the complete transfer matrix of the system is

the product of the individual transfer matrices. For TE wave, each single cell

has a transfer matrix according to TMM and is given by:

3

11 12

21 22 1

sincos

sin cos

ll

ll

l l l

iM M

nM dM M

in x

(16)

Where l represents either dielectric or liquid crystal layer. The phase l is

expressed as l

llll n

ddk

2 for the entire structure of dielectric/LC

/dielectric, after temperature effects the l given by:

0

2 cosl l l l l

l

n n d d

(17)

Where ld , ln , ln and 0 represents the dielectric and liquid crystal layer

thicknesses, refractive index, refractive index variation and the free space

wavelength respectively. For the entire structure of (D/LC/D)N, the total transfer

matrix is given by:

( )ND DLCT M M M (18)


Where N is the number of cells, and the matrix elements can be obtained in

terms of the elements of the single-period matrix. The transmission coefficient

for tunneling through such a structure is given by:

2 211 22 12 21

4

( ) ( )t

T T T T

(19)

where ijT are the elements of the matrix T .

3. RESULTS AND DISCUSSION

In this one-dimensional ternary D/LC/D photonic crystal, we use four structures

22 /35/ CaFUCFSiO , 22 /5/ CaFCBSiO , 53/35/51 NPSKUCFNFK and 53/5/51 NPSKCBNFK .

The temperature dependence of PBG for normal incidence of TE light on one-

dimensional binary structures with 20N period at liquid crystalline phase

temperatures without any alignment is shown in Figs. (2) – (8).

450 500 550 600 650 700 7500

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

wavelength (nm)

tra

nsm

issio

n

T=320 (0K)

T=340 (0K)

T=360 (0K)

T=320 (0K)

T=340 (0K)

T=360 (0K)

Sio2/UCF-35/CaF2d1=d2=d3=50 nmsolid line (no)dotted line (ne)

Fig. 2. Transmission PBG for 22 /35/ CaFUCFSiO structure with N=20 and

o0

Fig. (2) shows that the increase in temperature, PBG increase and shifts to red

wavelength. The PBG for extraordinary ray (ne) is very large than ordinary ray

(no). Temperature dependence of transition light for 22 /5/ CaFCBSiO structure is

plotted in Fig. (3). The results represent for ne situation PBG width is very vast

and variations of figure with respect temperature in the right side of gap is very

sharp.


450 500 550 600 650 7000

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

wavelength (nm)

tra

nsm

issio

n

T=260 (0K)

T=280 (0K)

T=300 (0K)

T=260 (0K)

T=280 (0K)

T=300 (0K)

Sio2/5CB/CaF2d1=d2=d3=50 nmsolid line (no)dotted line (ne)

Fig. 3. Transmission PBG for 22 /5/ CaFCBSiO structure with N=20 and

o0

Figure (3) shows that with increase of temperature, PBG increase and shifts to

red wavelength. The PBG variations of structure with based UCF-35 liquid

crystal for long wavelength is noticeable, but for 5CB liquid crystal this result is

obvious for short wavelengths.

Table 3. PBG with temperature and refractive index (ne or no) for 22 /35/ CaFUCFSiO and

22 /5/ CaFCBSiO

PBG Width

(

(

(

PBG (nm) )( KT O PBG Width

(

(

(

PBG (nm) Structure

ne no

212.2

506.2-718.4 320 147.7 488.7-636.4

205.4 507.4-712.8 340 149.4 492.0-641.4 22 /35/ CaFUCFSiO

193.7 507.1-700.8 360 153.5 495.9-649.4

148.1 480.5-628.6 260 102.5 469.2-571.7

143.7 482.2-625.9 280 102.6 471.8-574.4 22 /5/ CaFCBSiO

135.9

483.0-618.9 300 104.2 474.8-579


Table (3) shows that PBG width of ne rays is broader than no rays, also with

temperature rise, in both structure, PBG increase and decreases for no and ne

respectively.

Figure (4) and (5) show the temperature effects on 53/5/51 NPSKCBNFK and

53/35/51 NPSKUCFNFK structures respectively. In figure (4) we see that PBG of

53/5/51 NPSKCBNFK construction with increasing of temperature increase

(decrease) for no (ne) state. One can see from figure (4), temperature rise shifts

band gaps to long and short wavelength for no and ne rays respectively, also for

the right side of PBG these shifts are clear obviously.

460 480 500 520 540 560 580 600 620 640 660 6800

0.2

0.4

0.6

0.8

1

wavelength (nm)

tra

nsm

issio

n

T=260 (0K)

T=280 (0K)

T=300 (0K)

T=260 (0K)

T=280 (0K)

T=300 (0K)

NFK-51/5CB/NPSK-53d1=d2=d3=50 nmsolid line (no)dotted line (ne)

Fig. 4. Transmission PBG for 53/5/51 NPSKCBNFK structure with N=20 and o0

450 500 550 600 650 700 7500

0.2

0.4

0.6

0.8

1

wavelength (nm)

tra

nsm

issio

n

T=320 (0K)

T=340 (0K)

T=360 (0K)

T=320 (0K)

T=340 (0K)

T=360 (0K)

NFK-51/UCF-35/NPSK-53d1=d2=d3=50 nmsolid line (no)dotted line (ne)

Fig. 5. Transmission PBG for 53/35/51 NPSKUCFNFK structure with N=10 and o0

Figure (5) shows that PBG of 53/35/51 NPSKUCFNFK configuration with

increasing of temperature increase (decrease) for no (ne) state. we can see from


figure (5), temperature increase moves band gaps to long and short wavelength

for no and ne rays respectively, but for the right side of PBG these shifts are

obvious.

Table 4. PBG with temperature and refractive index (ne or no) for 53/5/51 NPSKCBNFK

and 53/35/51 NPSKUCFNFK

PBG Width

(

(

PBG(nm) )( KT O PBG Width

(

(

(

PBG(nm) Structure

ne no

128.5 511.7-640.2 260 86.3 499.6-585.9

124.2 513.4-637.6 280 86.4 502.2-588.6

NFK51/5CB/NPS53

116.8 514.1-630.9 300 87.8 505.3-593.1

191.3 536.7-728 320 128.1 519.9-648

184.5 538-722.5 340 129.7 523.2-652.9 NFK51/UCF35/NPS53

173.1 537.8-710.9 360 133.7 527-660.7

Table (4) displays that PBG width of ne rays is broader than no rays, also with

temperature rise in both structures, PBG increase for no and decreases for ne.

4. CONCLUSION

In this paper, we use one-dimensional ternary D/LC/D photonic crystal for

structures 22 /35/ CaFUCFSiO , 22 /5/ CaFCBSiO , 53/5/51 NPSKCBNFK and

53/35/51 NPSKUCFNFK . The results show that in all four structures an

increase of temperature, PBG shifts to red wavelength, but an increase of

temperature PBG increase for no and decrease for ne. It is clear from figures and

tables the PBG for extraordinary ray (ne) is very large than ordinary ray (no),

also the results represent for UCF-35 liquid crystal PBG width is very vast and

variations of figure with respect temperature are very sharp. These variations for

22 /35/ CaFUCFSiO structure is more than other. PBG for SiO2 and CaF2 dielectric

structure great than NFK51 and NPSK35. We can use the proposed structure as


temperature sensing device, narrow band optical filter and in many optical

systems [15,20,22].

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